CBSE Class 11-science Answered

Determije its domqin also.

Asked by k.manju2007 | 18 Aug, 2015, 10:21: PM

Expert Answer

C o n s i d e r space t h e space f u n c t i o n space f colon R rightwards arrow R comma space d e f i n e d space a s f open parentheses x close parentheses equals fraction numerator x squared over denominator 1 plus x squared end fraction D o m a i n space i s space t h e space s e t space o f space a l l space v a l u e s space t h a t space x space c a n space a s s u m e space s u c h space t h a t space f left parenthesis x right parenthesis space i s space d e f i n e d. F r o m space t h e space d e f i n i t i o n comma space i t space i s space c l e a r space t h a t space f left parenthesis x right parenthesis space i s space d e f i n e d space f o r space a l l space v a l u e s space o f space x. H e n c e space d o m a i n space o f space f space i s space t h e space r e a l space n u m b e r space s e t space R. R a n g e space i s space t h e space s e t space o f space a l l space v a l u e s space t h a t space y space c a n space a s s u m e comma space w h e r e comma space y equals f open parentheses x close parentheses S i n c e space x squared space i s space p o s i t i v e space a n d space left parenthesis 1 plus x squared right parenthesis space i s space p o s i t i v e comma space y greater than 0 A l s o comma space x squared less than 1 plus x squared T h u s comma space fraction numerator x squared over denominator 1 plus x squared end fraction less than 1 H e n c e comma space w e space h a v e comma space 0 less or equal than y less or equal than 1 T h u s comma space r a n g e space o f space f left parenthesis x right parenthesis space equals open curly brackets y element of R colon 0 less-than or slanted equal to y less than 1 close curly brackets

Answered by Vimala Ramamurthy | 19 Aug, 2015, 09:30: AM

CBSE Class 11-science Answered

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CBSE Class 11-science Answered

Concept Videos

Ordered pairs, cartesian products of sets

Relation between two sets

Functions and various forms of representation

Graphs of special types of functions

Ordered pair and cartesian product of sets

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